P. Viot et al., NEAREST-NEIGHBOR FUNCTIONS IN A ONE-DIMENSIONAL GENERALIZED BALLISTICDEPOSITION MODEL, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 57(2), 1998, pp. 1661-1667
We derive exact expressions for the nearest-neighbor probability funct
ions for configurations of disks on a line generated by a generalized
ballistic deposition process. The presence of clusters of disks profou
ndly modifies the nearest-neighbor functions compared with those of cl
uster-free configurations. We generalize theorems on ergodic ensembles
of isotropic packing of particles to cases where clustering of partic
les occurs.